A variational formula on the Cramér function of series of independent random variables
Krzysztof Zajkowski · Positivity · 2016
In (Zajkowski, Positivity 19:529–537, 2015) it has been proved some variational formula on the Legendre–Fenchel transform of the cumulant generating function (the Cramér function) of Rademacher series with coefficients in the space $$\ell ^1$$ . In this paper we show a generalization of this formula to series of a larger class of any independent random variables with coefficients that belong to the space $$\ell ^2$$ .